Advance Journal of Food Science and Technology 6(10): 1143-1146, 2014
ISSN: 2042-4868; e-ISSN: 2042-4876
© Maxwell Scientific Organization, 2014
Submitted: ‎
July ‎24, ‎2014
Accepted: September ‎13, ‎2014
Published: October 10, 2014
Application of Statistical Analysis Software in Food Scientific Modeling
1
Miaochao Chen, 2Kong Xiangsheng and 1Kan Chen
Department of Mathematics, Chaohu University, Hefei, 238000, P.R. China
2
Department of Computer and Information Engineering, Xinxiang University,
Xinxiang City, Henan Province, P.R. China
1
Abstract: In food scientific researches, sophisticated statistical analysis problems often can be met and in this study,
through SPSS statistical analysis software, the method of the curve regression model and the multiple regression
model that both are common in food science has been established and the experimental results show that the method
can be effectively used in the statistical analysis model of food science.
Keywords: Food science, modeling, SPSS statistical analysis software
INTRODUCTION
SPSS is a widely used program for statistical
analysis in social science. It is also used by market
researchers, health researchers, survey companies,
government,
education
researchers,
marketing
organizations, data miners and others. The original
SPSS manual (Nie et al., 1970) has been described as
one of "sociology's most influential books” for allowing
ordinary researchers to do their own statistical analysis.
In addition to statistical analysis, data management
(case selection, file reshaping, creating derived data)
and data documentation (a metadata dictionary is stored
in the data file) are features of the base software (Du
and Ke, 2013).
In food science searches, the sample sources are
complex, the production processes are various and there
are many links of quality control measures of
processing (Eke et al., 2013). In order to save a lot of
manpower and material resources, speed up the
development of new products and control the quality of
products better, the important problems for food
scientific researchers that must be solved are to
establish the corresponding mathematical model and
reveal universal natural laws. However, if we use the
traditional statistical analysis method to analyze and
process the experimental data and set up a mathematical
model, the calculation process will be very
complicated. On the basis of being engaged in
experimental design and the teaching of statistical
analysis for a long time, the authors of this study
combine the actual problems in food scientific
researches and give the introduction of the application
of SPSS statistical software in the modeling of food
scientific researches as follows (Jiwen et al., 2013).
Fig. 1: The relationship of the specific activity between
substrate concentration and enzyme
MATERIALS AND METHODS
In the problems of food scientific researches,
sometimes two variables have a linear relationship, but
in most cases, they always haven’t a linear relationship
but a nonlinear relationship. For example, when making
a Michaelis-Menten equation and the calculation of
Michaelis-Menten constants, we can measure the
relationship between the specific activity of enzyme
and the substrate concentration and get the 9 pairs of
data as shown in Table 1. Make the scatter diagram
with these data (Fig. 1) and we can see that the
distribution of these points is in a curve shape (Zhao
et al., 2011).
The basic task of curve regression analysis is to
establish a curve regression equation through the actual
observation data of the two correlated variables x and y
so as to reveal the form of the curve relation between x
and y. There are usually three ways to determine the
type of the curve relationship between x and y: first, use
professional knowledge as well as the known
theoretical laws and practical experience; second, when
Corresponding Author: Kan Chen, Department of Mathematics, Chaohu University, Hefei, 238000, P.R. China
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Adv. J. Food Sci. Technol., 6(10): 1143-1146, 2014
Table 1: Measured values of the research of the reasons of non-enzymatic browning in the manufacturing process of a brand of peach juice
Non-enzymatic browning
Determination No. Ieucoanthocyanin X1 Anthocyanin X2
Maillard reaction X3
Ascorbic content X4
package value y
1
0.045
0.032
0.008
2.654
9.520
2
0.063
0.013
0.007
2.891
8.960
3
0.054
0.025
0.005
3.251
8.420
4
0.062
0.012
0.004
3.218
8.320
5
0.060
0.009
0.013
2.854
7.650
6
0.053
0.016
0.011
3.264
7.850
7
0.041
0.021
0.015
2.785
7.210
8
0.074
0.011
0.008
3.216
8.470
9
0.046
0.015
0.021
3.518
9.460
10
0.065
0.021
0.018
2.920
10.910
11
0.071
0.016
0.017
3.464
12.410
12
0.094
0.012
0.011
3.217
9.760
13
0.048
0.015
0.021
2.768
8.320
14
0.057
0.021
0.017
3.276
7.870
15
0.021
0.013
0.013
2.896
7.980
16
0.095
0.021
0.011
3.217
8.120
there’s no theoretical law and practical experience to be
used, use the point depiction method to draw the actual
measuring points on the paper with rectangular
coordinates and observe the nearest function curve of
the distribution trend of the actual measuring points and
then use the function relation and make it matching
with the curve relation; third, in the SPSS viewer, make
judgment according to the squared value of the
correlation coefficient and the larger the squared value
of the correlation coefficient is, the better the model
will be Zagorska et al. (2011).
Curve regression analysis:
Step 1: Input the data in Table 1 into SPSS data editor,
select “Analyze-Regression-Curve Estination”
in turn as shown in Fig. 2 and then the dialog
box of (Curve Estination) can be opened.
Step 2: Select the variable “ ” and enter into the box of
“Variables”. Make “Y” enter into the box of
“Dependents”. And in the column of “Models”,
select all the options and press (OK) to end it.
In the column of “Models”, there are 11 kinds of
fitting models and the function expression that is
represented by all model options is as follows.
For the option of Linear, use a linear model for
fitting and the model is: y = b 0 + b 1 x.
For the option of Quadratic, use a quadratic
polynomial for fitting and the model is: y = b 0 + b 1 x +
b 2 x2.
For the option of Compound, use a complex model
for fitting and the model is: y = b 0 (b 1 )x.
For the option of Growth, use a growth model for
fitting and the model is: 𝑦𝑦 = 𝑒𝑒 (𝑏𝑏0 + 𝑏𝑏1 𝑥𝑥) .
For the option of Logarithmic, use a logarithmic
model for fitting and the model is: y = b 0 + b 1 ln (x).
For the option of cubic, use a cubic polynomial for
fitting and the model is: y = b 0 + b 1 x + b 2 x2 + b 3 x3.
For the option of s, use a s curve for fitting and the
model is: y = exp (b 0 + b 1 ) /x.
For the option of Exponential, use a logarithmic
model for fitting and the model is: 𝑦𝑦 = 𝑏𝑏0 𝑒𝑒 𝑏𝑏1 𝑥𝑥 .
For the option of inverse, use a hyperbolic curve for
fitting and the model is: y = (b 0 + b 1 ) /x.
For the option of Power, use a power exponent
model for fitting and the model is: y = b 0 𝑥𝑥 𝑏𝑏1 .
For the option of Logistic, use a logic model for
fitting and the model is: y = 1/ (1/u + b 0 b 1 x).
Multiple regression analysis: In food scientific
researches, there are many independent variables that
can affect the dependent variable y. For instance, the
factors that affect the quality of food products include
the processing temperature, the pressure of sterilization,
the time of sterilization, PH value, etc. Thus, it is
necessary to further discuss the regression of 1
dependent variable and several independent variables as
well as the relevant problems (Wythe et al., 2013). The
basic task of multiple regression analysis is to establish
the regression equation between the dependent variable
and all the independent variables according to the actual
observation values of all dependent variables and
independent variables so as to reveal the specific form
of the relation between the dependent variable and all
the independent variables and the purpose is to use the
established regression equation for prediction and
control. The calculation of multiple regression analysis
is complex and SPSS software can make the
computational process “a fool”. For example, in the
research of the reasons of non-enzymatic browning in
the manufacturing process of a brand of peach juice, the
ieucoanthocyanin (X1), anthocyanin (X2), Maillard
reaction (X3) and non-enzymatic browning package
value (Y) and the results are shown in Table 1 and now
we make regression analysis on the relationship between
Y and X1, X2 and X3:
Step 1: After input the data in Table 2 into SPSS data
editor, select “Analyze-Regression Linear” in
turn as shown in Fig. 3 and then the dialog box
of (Linear Regression) can be opened.
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Adv. J. Food Sci. Technol., 6(10): 1143-1146, 2014
Table 2: Summary table of models
Change statistics
--------------------------------------------------------------------------------Sig. F
2
2
Model
R
R
Adjusted R
S.E.E.
R2 change
F change
df1
df2
change
1
0.821
0.674
0.651
0.86640
0.674
28.971
1
14
0
2
0.885
0.784
0.751
0.73227
0.110
6.598
1
13
0.023
3
0.939
0.882
0.853
0.56235
0.098
10.044
1
12
0.008
a predictors: (constant) X2; b predictors: (constant) X2 X1; c predictors: (constant) X2 X1 X4; d dependent variable: Y; S.E.E.: Standard error of
the estimate
Table 3: Output results of the curve regression
Model summary
---------------------------------------------------------------------------------Equation
R2
F
df1
df2
Sig.
Linear
0.691
15.639
1
7
0.005
Logarithmic
0.886
54.382
1
7
0.000
Inverse
0.984
435.179
1
7
0.000
Quadratic
0.923
35.739
2
6
0.000
Cubic
0.986
115.349
3
5
0.000
Compound
0.592
10.172
1
7
0.015
Power
0.809
29.638
1
7
0.001
S
0.962
179.038
1
7
0.000
Growth
0.592
10.173
1
7
0.015
Exponential
0.594
10.172
1
7
0.015
Logistic
0.591
10.170
1
7
0.015
Step 2: Select the left “Y” into the right “dependent
(dependent variable), select “X1”, “X2”, “X3”
and “X4” into the right “Independent”
(independent variable and select “Stepwise
(stepwise regression method)” in the “Method”
here, Enter, Forward, Backward and other
methods also can be selected, tut the results are
different as shown in Fig. 4.
Step 3: After pressing the button (statistic⋯), it is as
shown in Fig. 5, check “Estimates” (estimated
value), “Confidence intervals (confidence
interval)”, “Modelfit” (test of goodness of fit of
regression model), “Rsquared change (square of
correlation coefficient)” as well as the residual
“Durbin Watson” and then click the (Continue)
button to go back to the dialog box of (Linear
Regression) and press (OK) to end it.
RESULTS AND DISCUSSION
Curve regression analysis: The output results are
shown in Table 3.
In the above results, the meaning of each column
of data is:
•
•
•
•
•
•
•
•
Dependent Variable: dependent variable
Equation: the selected model used for fitting
R Square: the squared value of the correlation
coefficient
F: F value
dfl and df2: degree of freedom
Sig: significance level
Constant b0: constant term
bl-b3: the fitted values of the undetermined
coefficients in the model
Parameter estimates
------------------------------------------------------------------Constant
b1
b2
b3
24.337
4.373
18.697
20.686
68.286
-64.850
2.534
17.289
-1.190
-19.443
36.714
-5.509
0.264
24.459
1.119
20.755
0.551
4.378
-1.787
3.197
0.113
24.459
0.113
0.041
0.893
The results in Table 3 are the optimal fitted results
of all models and the advantages and disadvantages of
all models can be compared by comparing the squared
values (R Square) of the correlation coefficients. The
larger the squared values of the correlation coefficients
are, the better the model is. In CUB (the cubic
polynomial model), Rsq = 0.986, namely the squared
value of the correlation coefficient is bigger, so
choosing this kind of model for fitting is the most
appropriate. The model of adopting the cubic
polynomial for fitting is:
y=
−19.443 + 36.714 x − 5.509 x 2 + 0.264 x 3
Multiple regression analysis: Table 2 is the summary
table of models. In the table, every step of the
correlation coefficient (R), the square of the correlation
coefficient (R Square), the adjusted square of the
correlation coefficient (Adjusted R Square), the standard
error of estimate (Std. Error of the Estimate) and the
change statistics (Change Stat cs) including the square
of the correlation coefficient (R square Change), F value
(F Change), the first degree of freedom (df), the second
degree of freedom (df2) and the significant possibility
(Sig. F Change) etc., have been listed. The footnote
under the table shows every step of item used for
prediction (including independent variables and constant
terms).
Table 2 is the table of coefficient analysis. In the
table, every step of constant terms and the
corresponding un-standardized coefficients have been
listed, including the values (B) and the standard error
(Std Error) of the coefficients of constant terms and
variables, Beta value of standardized coefficients, t
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Adv. J. Food Sci. Technol., 6(10): 1143-1146, 2014
value and the significance level (Sig.) and the values of
the undetermined coefficients of independent variables
and the confidence interval of 95% of constant terms
(95% Confidence Interval for B).
Based on the above information, we can obtain the
multiple regression equation by the stepwise regression
method:
y=
−79.641x1 + 207.215 x2 + 1.491x4 + 5.484
and the correlation coefficient of the model i 0.939.
REFERENCES
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Note: Provide us missing Figure 2 to 5 which are
mentioned in the text but not available with
file.
Note: At end note of Table 2 “a, b, c, d” are
explained while not mention anywhere in
Table 2
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